The objective of this paper
is to adapt the theory of saturation as developed by Oscar Zariski to the case of
k-analytic rings. For the most part k is an algebraically closed field of positive
characteristic. We think that saturation can be helpful in the definition of
equisingularity. The results beneath show that some necessary conditions for such a
task are fulfilled in this particular case. We do however not go so far as to actually
define equisingularity.